So for the broadest range of questions that may arise – be they queries about the kashrut of microbial enzymes, or the use of a shaliah le-kabbalah in giving a get, or the permissibility of driving on Shabbat to be a shomer for a corpse – the teshuvot are bound to be written in the positivist style. In addition to there being many good reasons to reason this way, there are, in the large majority of cases, no good grounds not to. We are all positivists in the same way that we all use Euclidean geometry and Newtonian mechanics to solve the broadest range of problems in the configuration of space and in the dynamics of motion. Euclid and Newton are not only perfectly suited to the small scale of the billiards table; their relative simplicity and linear quality serve us well in most of the tasks we face. But despite the fact that Euclid and Newton are splendid and irreplaceable tools in most ordinary matters, we need to know that their “local success” does not necessarily translate into “global success”. When Einstein measured, during a solar eclipse, the light of a distant star that passed very near the large mass of the darkened sun, he demonstrated that we either had to concede that space was not Euclidean, or that light did not travel in straight lines near large gravitational fields. We know, in other words, that there are those phenomena that lie outside the domain of normal observation, that lay bare to us the need for more sophisticated, less simple tools of analysis that can be extremely disorienting at first. But that is the only way that progress is made.

This is the sense in which we are all positivists in law. It is a splendid and irreplaceable tool for the ordinary questions that law is called upon to answer. But then there are the analogues of Einstein’s landmark experiment, the hard cases of law, hard cases like the one before us in this paper. For we are dealing with a case in which the logic of the system and its precedents do not fit well with the personal experiences and narratives of gay and lesbian Jews, and with the growing moral senses of the community.

As far as I am aware, the physics is entirely correct. Classical mechanics is an elegant and internally consistent theory. It also happens to match up well with the physical universe, for a limited range of cases. These properties don't necessarily have to coincide -- one could come up with elegant and consistent theories that have no relationship to physical reality (like a universe in which F=mj, or heck, this is what they once thought non-Euclidean geometry was), and though we assume that physical reality is consistent (or else all bets would be off when it comes to science), it's not necessarily going to obey the simplest or most elegant laws possible.

And, in fact, the correspondence between classical mechanics and physical reality falls apart when you look at very small or very large things, travel at high velocities, etc. Classical mechanics as a theory is unharmed, and continues to be useful in the same cases in which it was useful, but new theories (quantum mechanics; special and general relativity) are required to describe the physical universe in those other domains of observation.

So Tucker is making this same point about halacha. (I'm not sure I agree with him -- i.e. my own views are even less "Newtonian", i.e. the opposite reason from why the other teshuvot submitted to the CJLS would disagree with him --but my opinions are beyond the scope of this post.) He would define a "classical" theory of halachic jurisprudence that is useful in everyday cases, but recognize that this theory does not correspond to reality in all cases, and develop another theory that applies to those cases.

Another point that Tucker doesn't mention but that may strengthen his analogy: The "exceptions" to classical mechanics aren't just freak occurrences, but appear all the time. For example, atoms and molecules can't be explained with classical mechanics, and require quantum mechanics. Many famous things are made of atoms and molecules! Likewise, gay and lesbian people aren't anomalous; they're everywhere.

Question for Rabbi Tucker: Certainly, it's not convenient to use relativity or quantum mechanics to describe everyday situations at human scales (between atoms and galaxies), but it's possible. The correspondence principle says that quantum mechanics reduces to classical mechanics for large enough systems. Likewise, special and general relativity reduce to classical mechanics when v << c (velocity is much less than the speed of light) and we're looking at small masses and small chunks of space. Does your "enhanced halakhic method" obey an analogous correspondence principle? That is, if only the enhanced method were applied, would it arrive (albeit via more effort) at the same results as the positivist method would (in the cases for which you think a positivist approach is valid)? And if not, then would complementarity be a better physics analogy?

***

Going back to the physics, in addition to the obvious reasons why classical mechanics is useful even though "more correct" theories exist (an engineer building a bridge doesn't need or want to consider relativistic effects, which would make the calculations much more difficult), there are also pedagogical reasons for this, which are foremost in my mind as a high school physics teacher.

And maybe these reasons aren't so different: similar to the (discredited) theory that ontogeny recapitulates phylogeny, perhaps individual science learning recapitulates scientific development. For my master's project in science education, I looked at how students' mental models undergo Kuhnian paradigm shifts. (This idea wasn't original, and the conditions for a paradigm shift appear in a 1982 article in Science Education by George J. Posner et al., but I was looking more closely at the mechanism of this paradigm shift and the "reactive intermediates".)

So just as classical mechanics had to be developed before Einstein could come up with relativity or Schrodinger could come up with wave mechanics, perhaps students need a foundation in classical mechanics before they can understand "modern physics".

Some students who come into first-year physics with lots of enthusiasm about the subject struggle because they're not able to bracket the "hard cases" while first looking at a simplified model. We make simplifications all the time, and not just the kind where we use classical mechanics instead of quantum mechanics or relativity: high school physics is filled with frictionless surfaces and massless strings and rigid bodies and point masses and point charges and elastic collisions and negligible air resistance and negligible electrical resistance and such. Some students are always asking "But wouldn't it break?" or "But what about the curvature of the earth?" or "What if you were going near the speed of light?". And those are excellent questions to ask. After you get the basic concept and are ready to consider more advanced applications. But if you don't allow for some approximations on the way there (like the famous spherical chicken), you'll be paralyzed and will never gain mastery of the basic concepts. (One of my colleagues had to say to a freshman physics class "Einstein was never born!") It's important to ask questions all the time, and it means that these students are thinking seriously about how physics applies to the real world and not just plugging-and-chugging by rote, but it's also important to learn how to use a simplified model to come up with an approximate answer, and then evaluate this result to see whether it's close enough or whether we have to consider other parameters.

Sometimes this process occurs during first-year physics itself. When we start in the fall, we assume that Earth's gravitational field is uniform (so gravitational acceleration is constant, gravitational potential energy is simply mgh, etc.), and then in December or so, we do the "gravity" unit and see what happens when you get far away from Earth's surface that you can't assume that g is always 9.8 m/s2 anymore.

That said, there's still some value in giving students a taste of more "advanced" physics even if they're not going to get all the way there from first principles, because these theories are such an essential part of our current understanding of the physical universe. Even though high school students certainly aren't going to master classical mechanics to the level that Einstein understood it just before publishing his groundbreaking papers in 1905, they should still get some appreciation of physics developments of the last century. For example, the standard Regents curriculum includes the Bohr model and a superficial look at the Standard Model. If there were more time in the school year, I would go further -- I would love to develop a way to teach quantum mechanics concepts (not the Bohr model, but the real thing) to first-year physics students, and I already do relativity with my AP students after the AP test.

So the point is that in physics education, there is a place both for using simplified models and looking beyond those models.

As I learned today from a student, we're not even consistent in the simplified models that we teach. In AP, we've been doing integrals to find the electric fields due to various charge distributions, and a student asked an excellent question: if charge is quantized, then what does "dq" (an infinitesimal amount of charge; essential for setting up an integral) mean, and how can we talk about these continuous charge distributions? She was totally right. We teach from the beginning (starting way back in chemistry) that charge is quantized, and there are these discrete little charged particles. But then we teach classical electromagnetism, which is really all about continuous charge distributions, with concepts like (finite) charge density. (Note: Maxwell's equations predate the discovery of the electron!) So the answer is that when we're talking about an infinite line of charge with linear charge density λ, we're ignoring the fact that charge is quantized and operating within a theory in which it isn't, and then we can argue that this is close enough to our universe when we're looking at macroscopic things, since the quantum of charge is really really small on that scale. (And "infinite" really just means that L >> r.)

So do these rantings about physics pedagogy have any analog in the study of halacha? Perhaps the introductory Talmud student who is always asking "Did they really have to sacrifice an animal? That's sick and inhumane!" and "Does God really care?" and "Where are all the women?" is analogous to the introductory physics student who is always asking "But isn't light also a particle?" and "What about air resistance?" and "What about the rotation of the earth?". That is, they're both asking very very important questions (you'll have a hard time designing an airplane if you never stop ignoring air resistance!), but in order to develop an understanding of Talmudic methodology / physics methodology (which will assist later on in answering those important questions), it may be helpful to put aside those questions temporarily and focus on one thing at a time.

On the other hand, it's also important to develop, from the beginning, some understanding of the more complex questions, and to begin grappling with those questions, so that the student of halacha/physics understands that halacha/physics is not just a formal system or an intellectual exercise, but is intended as a model for the real world.

(modeln. 1. a systematic description of an object or phenomenon. 2. a standard or example for imitation.)

11 comments:

However, I don't think Einstein himself measured the deflection of light from stars during an eclipse. In fact, I think there is a famous (possibly apocraphal) anecdote in which someone handed him a telegram with the results of the observation confirming general relativity, and he didn't even bother to read it--he was sure his theory was right, regardless of observations. I guess from a scientist's point of view it really shouldn't matter who made the actual measurements if they are correct (it only matters who made them when they are incorrect), but from a historian's point of view it always matters who made the measurements, because we don't care whether they are true.

I'll get off my history of science soap box now, I just figured, as long as we are being meta...

And, Gordon, if you are actually reading this, congratulations on the award.

However, I don't think Einstein himself measured the deflection of light from stars during an eclipse.

Good call - how did I not catch that? Einstein never did an experiment in his life.

But this experiment in 1919 paved the way for Einstein winning the Nobel Prize in 1921. (You can't win a Nobel Prize for a theory until it's experimentally confirmed. I knew the person who did the experiments confirming the Marcus Theory so that Marcus could win the Nobel Prize in Chemistry in 1992 for a theory he had developed in the '50s.)

For that matter, how does secular law decide when to "switch gears"? For example, the Wiki on legal positivism mentions a case in which...

"principle trumped law. The case held that a murderer cannot inherit his victim's property, despite the fact that the victim's will said unambiguously that the murderer was the heir, and the statute of wills said the will was valid and should be carried out."

One could beg the question by saying that, in secular law, principle trumps law whenever judges decide it does. However, I would think there are well-defined procedural norms that govern the apellate process, even if that apellate process is ultimately motivated by (extralegal) ethics. I just don't know what those norms are nor whether halakha has any counterpart. (I'm one of those beginning talmud students who is always asking whether God really cares one way or the other...)

I believe it was Eddington who confirmed Einstein's theory of general relativity in 1919.

I fail to see the benefit of using the analogy of classical/ quantum physics with halakha.

Both classical and quantum physics are subject to scientific hypothesizing and then falsification. There is no way to scrutinize halakha as science at all. If halakha has a rationale, it is either as an aesthetic lifestyle or as a historical development ( what have Jews traditionally done with mourning? with diet? etc.)

It seems difficult to justify using the understanding of the universe that studying physics provides us to point out the limits of halakha. The four cubits and the lifestyle contained within the walls were not developed scientifically; they were either the result of a Revelation at Sinai that most certainly would fail Popper's falsibility test or the result of organically developed folkways of a people that developed over centuries.

Now, if Tucker wanted to compare Aggadah and the resultant metaphysical speculation of the Sages and kabbalists with string theory, that might have been interesting.

Sure, there are some differences between physics and halakha, but don't let them blind you to the similarities.

First, may I suggest you put aside for a moment your notions of what makes either halakha or physics "true." When you do that, you are looking at them sociologically--as systems of knowledge that reside with large and diverse communities of experts considered qualified to produce and interpret that knowledge.

As for the analogy, it has less to do with the content of either the physics or the halakha and more to do with how the members of respective communities of experts accomodate a paradigm shift.

Physics accomodated the paradigm shift from Newtonian to relativistic mechanics partly by seeing relativity as an enlarged mechanics of which Newtonian mechanics had "always" (as it were) been a good approximation for ordinary scales. What might seem like an incompatibility between the old system and the new was resolved by placing the old system within the new and continuing to use the old system for a large class of applications, albeit with a new recognition of its limitations.

What Tucker is suggesting is that halakha undergo a similar paradigm shift to resolve the conflict between the positivist ban on homosexuality and the ethical need to wholly embrace homosexual members of the community. He is suggesting that we look at positivism as a special case, a useful approximation that works for common applications of halakha. You may not see the positivist reading of leviticus on the one hand and the ethical need to embrace queer jews on the other as "observable facts" on par with those of science. But socialogically they are functioning the same way: as opposing facts that need to be reconciled. (To the communities affected, these facts are VERY real.) And I think the analogy to the paradigm shift in physics is quite apt in this case, since it suggests a way forward that actually preserves the positivist method for most applications.

A nice post, with lots of thought-provoking material on physics pedagogy. I only hopped over to your blog following the link in my daughter ALG's blog to your Indian restaurant spoof, then noticed this heading, and took a look at it. I'm glad I did.

Tucker didn't quite get all the physics exactly right. It's not quite true that Newtonian physics would have predicted no bending of the light. A reasonable interpretation of Newtonian physics would have predicted that light would fall in the sun's gravitational field, as it passed the sun, at the same acceleration as any other body. If so, the light rays would bend exactly half as much as Einstein predicted, and as Eddington observed them to. That "classical" bending could be understood, in the context of general relativity, as due to the curvature of time. The additional bending, predicted by Einstein but not by Newtonian physics, can be understood as due to the curvature of space associated with the sun's gravitational field.

Interestingly, in earlier versions of general relativity, published before 1915, Einstein predicted that light would bend only half as much as he later predicted. A German expedition to test that prediction set out in July 1914 to observe a total eclipse in Russia in September 1914. You can imagine what happened to this group of Germans, carrying telescopes and fancy cameras, when they found themselves in Russia in August 1914. They were arrested as spies, and, though they were eventually released, they missed the eclipse. Meanwhile, Einstein corrected his calculation, and published his final prediction of the bending of light in 1915. If World War I had broken out a couple of months later than it did, Einstein's 1915 prediction would have been merely an after-the-fact explanation for the failure of his earlier prediction, and he would never have become as famous as he did.

Einstein's 1921 Nobel Prize was not for general or special relativity, but for explaining the photoelectric effect, so the 1919 eclipse observations had no direct effect on the Nobel Committee. But no doubt his greatly increased fame, resulting from the 1919 eclipse observations, put pressure on them to give him a Nobel Prize for something.

You mentioned the continuous electric charge in Maxwell's equations as an approximation to the reality of quantized charge. There is some interesting pedagogy in that topic. It turns out that shot noise does not occur in electric currents in ordinary linear circuits, as you would naively expect from the magnitude of an electron's charge. It only occurs in nonlinear devices like transistors. I've never had time to sit down and figure out why. It may have something to do with the finite extent of the electron's wavefunction.

There is another analogy between physics and halacha, specifically between quantum mechanics and the halachic principles of rav and kavuah. See my posting in mail-jewish v52n08 on that topic, which you can find here: http://listserv.shamash.org/cgi-bin/wa?A2=ind0606&L=MAIL-JEWISH&P=R1193It was easy for me to find that posting because, sadly, it is the only hit you get if you search for "quantum" in the mail-jewish archives. But the search engine only seems to go back to 2004. There was a lot of discussion on that topic in mail-jewish around 1996.

It's not quite true that Newtonian physics would have predicted no bending of the light. A reasonable interpretation of Newtonian physics would have predicted that light would fall in the sun's gravitational field, as it passed the sun, at the same acceleration as any other body.

Why is this? It seems to me that Newtonian mechanics says that gravity is a force acting on objects with mass, and light (made of electric and magnetic fields) doesn't have mass.

"Why is this? It seems to me that Newtonian mechanics says that gravity is a force acting on objects with mass, and light (made of electric and magnetic fields) doesn't have mass."

Sure, formally the Newtonian expression for gravitational force on a body is proportional to its mass, so would be zero if the mass were zero. But the acceleration, for a given force, is inversely proportional to the mass, so the predicted gravitational acceleration would be 0/0, and you could not get a prediction of the degree of bending of light at all. A more reasonable approach would be to simply write an equation for the gravitational acceleration directly, in terms of the sun's mass and the distance from the sun. That expression would be independent of the mass, and could be used to make a prediction of the amount of bending. Newton himself, who thought of light as particles, rather than waves, would no doubt have done that.

Historically, it may be true that some people expected light not to be bent by gravity at all, before general relativity, but I don't think anyone would have been very surprised to find it that it accelerated by the same amount as any other body. What was surprising about Einstein's prediction is that light bends twice as much, implying that space itself is non-Euclidean.